The grip potential μ of a tire is defined, at a given instant, as being the ratio of the resultant of the longitudinal and lateral forces over the resultant of the vertical forces:
  μ  =                              F          x          2                +                  F          y          2                            F      z      
At a given instant, the maximum grip potential μmax of the tire on the ground is also defined as being the maximum value that the grip potential μ can take on. This maximum grip potential μmax depends on several factors including the nature of the ground (or the road) or its state of wear, the temperature of the ground and of the tire, or indeed weather factors involving, for example, the presence of water or snow on the ground.
The utilization percentage Pu of the maximum grip potential μmax of the tire is then defined by the following formula:
      P    u    =            μ              μ        max              ·    100  
This utilization percentage Pu corresponds to the percentage of the grip potential that is actually being used relative to the maximum grip potential. This value varies over the range from 0 to 100%. Naturally, the closer this value is to 100%, the greater the risk of the tire losing grip. Thus, the utilization percentage Pu serves to quantify utilization of maximum grip potential.
It is advantageous to quantify in real time the extent to which the maximum grip potential of each tire of a motor vehicle is being utilized in order to determine whether or not one of the tires is close to losing its grip with the ground. This information concerning tire grip can be transmitted to the driver of the vehicle so as to adapt driving accordingly, or to an electronic device for controlling the road holding of the vehicle.
Document WO 03/066400 discloses that the maximum grip potential μmax of a tire depends in particular on the following parameters:                the driving or braking force applied to the tire;        the lateral thrust force applied to the tire;        the load carried by the tire; and        the self-alignment torque, i.e. the moment about a vertical axis that is exerted by the tire.        
These various force parameters can be measured by means of sensors carried by the tire, in particular by means of sensors that measure the forces to which the walls or the rubbing strips of the tire are subjected.
The maximum grip potential can be deduced from those force measurements by training an approximation function, e.g. by training the weights of a neural network.
That known method of estimation turns out to be particularly complex to implement and requires complicated calibration of the tire and also close monitoring of variation in its parameters over time. As a result that method is expensive to implement in practice.